This is a phase I study to evaluate the safety, engraftment and relative survival of genetically engineered autologous CD34 peripheral blood progenitor cells (PBPC) in HIV+ persons undergoing therapy for non-Hodgkin's lymphoma (NHL). Adult subjects with AIDS and NHL will be eligible for this study if they had an initial response to chemotherapy and have CD4 counts 3 100/ml and are free of active opportunistic infections. After initial chemotherapy, subjects will undergo autologous PBPC transplantation. PBPC will be enriched from peripheral blood by mobilization with the cytokine G-CSF followed by apheresis. Prior to transplantation, two thirds of the apheresis product will be selected for PBPC, divided into two cultures, and grown on autologous stromal cultures for three days in growth medium containing the cytokines IL-3, IL-6, and SCF. During this time one culture will be transduced with a retroviral vector containing the anti-HIV double-ribozyme genes, which is directed toward the HIV tat and rev regions and the second culture will be transduced with a control vector that does not encode for a ribozyme. The two cultures of engineered cells will be mixed and infused into the subject. The untransduced stem cells will then be infused. Following infusions, the ratios of blood samples obtained at day +1 and months 1, 3, 6, 9, 12,18, and 24 and from marrow samples obtained at 1, 3, 6, 12, and 24 months. A relative increase in the frequency of cells containing the anti-HIV-1 TR/TAT ribozyme gene, compared to cells with the neutral marker gene, would imply that a selective survival advantage has been conferred to the cells by the anti-HIV-1 ribozymes. The specific aims of the study are: 1) to assess the safety and feasibility of administering PBPC transduced with retroviral vectors encoding an anti-HIV double ribozyme to HIV+ subjects undergoing intensive chemotherapy and stem cell transplantation for NHL. 2) To determine whether these genetically modified PBPC can engraft, differentiate, and circulate in the blood of transplanted recipients. 3) To determine the comparative survival of ribozyme-vector transduced PBPC progeny cells versus control vector marked cells in the periphery. 4) To evaluate the toxicity and disease-free survival of high dose chemotherapy with stem cell transplantation in HIV+ subjects with NHL.